Answer:
x = sqrt(10) - 9 or x = -9 - sqrt(10)
Step-by-step explanation by completing the square:
Solve for x:
x^2 + 18 x + 71 = 0
Subtract 71 from both sides:
x^2 + 18 x = -71
Add 81 to both sides:
x^2 + 18 x + 81 = 10
Write the left hand side as a square:
(x + 9)^2 = 10
Take the square root of both sides:
x + 9 = sqrt(10) or x + 9 = -sqrt(10)
Subtract 9 from both sides:
x = sqrt(10) - 9 or x + 9 = -sqrt(10)
Subtract 9 from both sides:
Answer: x = sqrt(10) - 9 or x = -9 - sqrt(10)
